Elsewhere in Syria, Russian and Syrian military officers told rebels in Eastern Qalamoun, about 25 miles northeast of Damascus, they must accept regime rule or leave.
The SANA news agency says two buses carrying the rebels left Douma on Monday morning, heading for Jarablus, a town in north Syria shared between rebels and Turkish forces.
The deal over Douma would mark the end of a weeks-long push by Assad's forces to consolidate their control over eastern Ghouta, just outside the capital.
The government offensive on Ghouta has been one of the deadliest of the war, killing more than 1,600 civilians, according to the Syrian Observatory for Human Rights.More news: MI basketball assistant Saddi Washington 'thankful' to be unharmed after auto accident
The last Syrian rebel group in eastern Ghouta near Damascus began withdrawing on Monday under an agreement with the government, state media said, though a military source said a group of insurgents were still rejecting the deal.
It said those on board were fighters and family members belonging to the Army of Islam, the largest rebel group in eastern Ghouta.
Following tough negotiations held between both parties, Jaish al-Islam and Moscow reached a final deal to evacuate fighters and civilians from the city of Douma, the last rebel-held bastion in the Eastern Ghouta enclave, opening the way for regime forces to capture the entire area.
Russian Federation has been a key backer of Syrian President Bashar Assad, ultimately helping to turn the tide of the devastating civil war in his favor.More news: A Sacramento Sheriff's Vehicle Hit a Protester During a Stephon Clark Vigil
The Army of Islam has refused to respond to media requests for comment.
Warning about UN's underfunded Syria operation this year, the adviser said only 7.7 percent of the United Nations humanitarian operation for Syria was funded after the first quarter of the year ended.
Assad, who has military support from Iran and Russian Federation, now controls the bulk of Syria, though it may be hard for him to recover much more territory without risking a collision with other foreign powers that have forces inside the country. More than 40,000 rebels and their family members have chosen to relocate, according to the Russian military.
Since 2016, the area had been controlled by the Jabhat al-Nusra (outlawed in Russia) and Jaysh al-Islam terror organizations, as well as the Ahrar al-Sham, Faylaq al-Ra·man and Fajr al-Umma groups linked to them. Turkey, with support from rebels, is running its own military operations against a US -backed Kurdish party that controls territory along the frontier.More news: Trump said to tell embattled EPA chief `we've got your back'
Abdul Karim also said that councils of some local towns are negotiating their own terms for reconciliation.